Transmission shaft for an aircraft turbine engine

Abstract

The invention relates to a transmission shaft (22) comprising: - a male cylindrical body (23), - a first splined section arranged coaxially around the male cylindrical body (23) and having longitudinal first splines (38) and comprising an alternation of first teeth (39) and first grooves (40), the first section (34) being rotationally fixed to the male cylindrical body (23), characterized in that the transmission shaft (22) further comprises: - a second splined section arranged coaxially around the male cylindrical body (23), the second section having longitudinal second splines and comprising an alternation of second teeth (44) and second grooves, the second section being stressed by an elastic element from a first position to a second position in which the second teeth (44) are angularly offset with respect to the first teeth (39).

Description

Technical field of the invention

[0001] The invention relates to a drive shaft for an aircraft turbomachine.

[0002] The invention relates in particular to a transmission shaft having splines. Technical background

[0003] An aircraft turbomachine typically extends along and around a longitudinal axis. It comprises a gas generator which typically includes, from upstream to downstream in the direction of gas flow in the turbomachine, a fan, a low-pressure compressor, a high-pressure compressor, a gas combustion chamber, a high-pressure turbine, and a low-pressure turbine.

[0004] The rotor of the low-pressure compressor is typically connected to the rotor of the low-pressure turbine via a low-pressure shaft. The rotor of the high-pressure compressor, on the other hand, is connected to the rotor of the high-pressure turbine via a high-pressure shaft.

[0005] The blower ensures the intake of an airflow that splits into a primary airflow passing through a primary channel and a secondary airflow passing through a secondary channel surrounding the primary channel. The primary airflow passes through the low-pressure and high-pressure compressors. The compressed primary airflow then passes through the combustion chamber where it is mixed with fuel. The combustion gases then pass through the high-pressure and low-pressure turbines. The energy of the gases is transformed by the turbine rotor of the low-pressure turbine into mechanical energy, which drives the rotation of the low-pressure shaft and, consequently, the low-pressure compressor.

[0006] Furthermore, such a turbomachine includes a variety of accessories such as lubrication pumps, fuel pumps, and electrical power supply components necessary for the operation of both the turbomachine and the aircraft. These accessories also require a power supply for their operation.

[0007] In this context, a portion of the turbomachine's mechanical energy is diverted to power the accessories. This diversion typically occurs at one of the turbomachine's shafts, specifically the high-pressure shaft. Such diversion is achieved via an accessory drive train, also known by the acronym ADT. This drive train is also used to mechanically drive the turbomachine during startup.

[0008] The accessory drive train typically includes drive shafts that ensure the transmission of rotational motion from the turbomachine shafts and the transfer of mechanical energy.

[0009] Each drive shaft extends along a longitudinal axis and typically comprises a male cylindrical body extending along the longitudinal axis and a female cylindrical body into which the male cylindrical body is coaxially engaged.

[0010] The male and female cylindrical bodies cooperate via a splined connection. The male cylindrical body comprises a section with longitudinal splines, and the female cylindrical body includes an internal annular housing with internal longitudinal splines that cooperate with the splines of the male cylindrical body. In some hybrid turbomachinery, the accessory drive train is also used for power injection phases. In such turbomachinery, the accessory drive train thus experiences alternating phases of power injection and extraction. This alternation of extraction and injection phases generates dynamic torques within the accessory drive train's transmission shafts, resulting in increased mechanical clearance between the splines of the male and female cylindrical bodies.These clearances are responsible for loud rattling noises during the rotation of the drive shafts. Furthermore, this alternating phase of power extraction and injection generates torque oscillations within the drive shafts.

[0011] These phenomena, which are particularly important in hybridized turbomachinery, can severely degrade the drive shafts.

[0012] For this purpose, there is a need to provide a drive shaft that limits mechanical play within the drive shaft and reduces torque oscillations. Summary of the invention

[0013] To this end, the invention proposes a drive shaft for an aircraft turbomachine, the drive shaft having a longitudinal axis and comprising: a male cylindrical body extending around and along the longitudinal axis, a first grooved section arranged coaxially around the male cylindrical body and having first longitudinal grooves regularly distributed around the longitudinal axis and comprising an alternation of first teeth and first grooves, the first section being rotationally fixed to the male cylindrical body.

[0014] The drive shaft is remarkable in that it also includes: a second grooved section arranged coaxially around the male cylindrical body, the second section having second longitudinal grooves regularly distributed around the longitudinal axis and comprising an alternation of second teeth and second grooves, the second section being stressed by an elastic element from a first position to a second position in which the second teeth are angularly offset with respect to the first teeth.

[0015] The invention may include one or more of the following features, taken individually or in combination with each other: The elastic element comprises at least one first spring mechanically connecting the first and second sections; the elastic element comprises a second spring diametrically opposite the first spring and mechanically connecting the first and second sections; the first section comprises an annular lateral flank having at least one first housing for receiving the first spring and optionally a second housing for receiving the second spring; in the second position, the second teeth are angularly offset by less than half a pitch relative to the first teeth, a pitch being the inter-tooth distance between two adjacent first teeth; at least one axial stop connected to the elastic means; a third section arranged coaxially around the male cylindrical body; the third section having longitudinal third grooves distributed around the longitudinal axis and comprising an alternation of third teeth and third grooves.the first section being arranged axially between the second and third sections, the third section being stressed by a second elastic element from a first position to a second position in which the third teeth are angularly offset relative to the first teeth, in the second position, the third teeth are angularly aligned with the second teeth, a female cylindrical body having an internal annular housing into which the male cylindrical body is inserted and internal longitudinal grooves cooperating with the first and second grooves, the internal grooves comprising an alternation of internal teeth and internal grooves, the first teeth being inserted into the internal grooves and the second teeth filling a defined angular gap between the first teeth and the internal teeth, the second teeth are pressed against the internal teeth.

[0016] The invention also relates to a method for preparing a transmission shaft according to any one of the preceding characteristics.

[0017] The process is also remarkable in that it comprises the following steps: (a) provide the male cylindrical body on which the first section is located, (b) provide the second section, and (c) apply the elastic means to drive the second section from the first position to the second position.

[0018] The invention also relates to a method of mounting a transmission shaft according to any one of the preceding characteristics.

[0019] The process is also remarkable in that it comprises the following steps: (a') prepare the transmission shaft according to the previous preparation process, (b') provide the female cylindrical body, and (c') insert the male cylindrical body into the female cylindrical body, the second teeth filling the defined gap between the first teeth and the internal teeth. Brief description of the figures

[0020] Other features and advantages will become apparent from the following description of non-limiting embodiments of the invention with reference to the accompanying drawings in which: there figure 1 is a longitudinal cross-sectional view of an example of an aircraft turbomachine according to the invention; the figure 2 is a schematic longitudinal cross-sectional view of a transmission shaft according to the invention, comprising a female cylindrical body and a male cylindrical body engaged in the female cylindrical body, the figure 3 is a cross-sectional view of the drive shaft of the figure 2 , according to plan A-A', the figure 4 is a schematic longitudinal cross-sectional view of the male cylindrical body of the figure 2 and indicating the assembly direction of the second and third grooved sections, the figure 5 is a schematic perspective view of the first section of the male cylindrical body, the figure 6 is a schematic cross-sectional view of the second segment of the male cylindrical body, the figure 7 is another schematic longitudinal cross-sectional view of the male cylindrical body, the figure 8 is a schematic cross-sectional view of the male cylindrical body along plane B-B', the figure 9 is a side view of the second section of the figure 6 . Detailed description of the invention

[0021] An example of an aircraft turbomachine 1 according to the invention is shown very briefly on the figure 1 . Turbomachine 1 is, for example, a turboprop.

[0022] The turbomachine 1 extends along a longitudinal axis X. An airflow F flows into the turbomachine 1.

[0023] For the purposes of the present invention, the terms "upstream" and "downstream" are understood relative to the direction of flow of the air flow F in the turbomachine 1 along the longitudinal axis X.

[0024] The turbomachine 1 comprises, from upstream to downstream, a blower 2, a low-pressure compressor 3, a high-pressure compressor 4, a combustion chamber 5, a high-pressure turbine 6 and a low-pressure turbine 7.

[0025] Each compressor 3,4 comprises a compressor rotor 3a, 4a and each turbine 6, 7 comprises a turbine rotor 6a, 7a. The compressor rotors 3a, 4a and the turbine rotors 6a, 7a are composed of a plurality of stages, each comprising a bladed wheel.

[0026] The compressor rotor 3a of the low pressure compressor 3 is connected to the turbine rotor 7a of the low pressure turbine 7 by a low pressure shaft 8. They form a low pressure body.

[0027] The compressor rotor 4a of the high-pressure compressor 4 is connected to the turbine rotor 6a of the high-pressure turbine 6 by a high-pressure shaft 9. They form a high-pressure body.

[0028] The low pressure shaft 8 and high pressure shaft 9 are centered on the longitudinal axis X and are free to rotate around the longitudinal axis X. The high pressure shaft 9 is arranged coaxially around the low pressure shaft 8.

[0029] The airflow F passes through the blower 2 and splits into a primary airflow F1 flowing through a primary stream v1 and a secondary airflow F2 flowing through a secondary stream v2 surrounding the primary stream. The primary airflow F1 passes through the low-pressure compressor 3 and the high-pressure compressor 4. The compressed primary airflow F1 then passes through the combustion chamber 5 where it is mixed with fuel. The combustion gases thus pass through the high-pressure turbine 6 and the low-pressure turbine 7. The energy of the gases is transformed by the turbine rotor 7a of the low-pressure turbine 7 into mechanical energy, driving the low-pressure shaft 8 and consequently, the low-pressure compressor 3.

[0030] The blower 2 comprises a rotating disk about the longitudinal axis X and blades 2a evenly distributed on the disk. The blower 2 is, for example, of the unshrouded type. Unlike a shrouded blower 2, the blower 2 does not include a blower housing surrounding the blades 2a. According to another example not shown, the blower 2 is of the shrouded type.

[0031] The disk is driven in rotation by a blower shaft 10. Advantageously, the blower shaft 10 is connected to the low-pressure shaft 8, for example, via a speed reducer 11. The speed reducer 11 is mechanical. It is, for example, an epicyclic or planetary gear train. While not shown, the speed reducer 11 conventionally comprises a sun gear and a ring gear centered on the longitudinal axis X. It also includes planet gears that mesh with the sun gear and the ring gear. Furthermore, it includes a planet carrier.

[0032] The solar element is rotationally fixed to the low-pressure shaft 8 and forms the input of the speed reducer 11, while either of the ring and the satellite carrier, depending on the configuration of the reducer 11, is rotationally fixed to the blower shaft 10 and forms the output of the speed reducer 11.

[0033] The speed reducer 11 allows the blower shaft 10 to be driven at a rotational speed lower than the rotational speed of the low-pressure shaft 8. This allows the dilution ratio of the turbomachine 1 to be increased.

[0034] The turbomachine 1 further includes an inter-compressor housing 12 arranged axially, with reference to the longitudinal axis X, between the low-pressure compressor 3 and the high-pressure compressor 4.

[0035] The turbomachine 1 may further include an inlet casing 13. The inlet casing 13 is arranged axially, with reference to the longitudinal axis X, between the blower 2 and the low-pressure compressor 3.

[0036] The turbomachine 1 may further include an inter-turbine casing 14. The inter-turbine casing 14 is arranged axially, with reference to the longitudinal axis X, between the high-pressure turbine 6 and the low-pressure turbine 7.

[0037] The turbomachine 1 may further include an inter-vein compartment v3 located between the primary vein v1 and the secondary vein v2.

[0038] Turbomachine 1 includes accessories or equipment (not shown) such as a fuel pump, a lubrication pump, an electric generator, an electric pump or a starter.

[0039] To drive these accessories, the turbomachine 1 typically includes an electric machine. The electric machine is particularly advantageously reversible. It is thus configured to draw power from a shaft, such as the low-pressure shaft 8 or the high-pressure shaft 9, and to inject power into another shaft, such as the low-pressure shaft 8 or the high-pressure shaft 9. The electric machine can therefore function as a generator when operating in a power-drawing phase and as a motor when operating in a power-injection phase.

[0040] To perform power extraction or injection, the turbomachine typically includes an accessory drive train 21, also known by the acronym ADT. The accessory drive train 21 comprises a gear train consisting of a series of interlocking gears, each mounted coaxially around a respective drive shaft. The gears of the gear train are driven by mechanical power extraction from the low-pressure or high-pressure shaft 8, 9, for example. The extracted mechanical power is transferred to the gear train via transmission shafts 22 coupled to one of the drive shafts. The gear train is also coupled to the rotors of the accessories or equipment.

[0041] With reference to figures 2 And 3 , each transmission shaft 22 has a longitudinal axis Z.

[0042] In the following description, the terms "longitudinal" and "longitudinally" are extended with reference to the longitudinal axis Z of the transmission shaft 22.

[0043] The transmission shaft 22 comprises a male cylindrical body 23 and a female cylindrical body 24.

[0044] Each male and female cylindrical body 23, 24 extends along and around the longitudinal axis Z. Each male and female cylindrical body 23, 24 thus has an elongated shape along the longitudinal axis Z. By "elongated", it is understood that each male and female cylindrical body 23, 24 has a length such that, measured along the longitudinal axis Z, it is greater than its internal diameter.

[0045] The male cylindrical body 23 is mounted coaxially at least in part in the female cylindrical body 24. The male cylindrical body 23 cooperates with the female cylindrical body 24 by means of a splined connection.

[0046] The female cylindrical body 24 extends longitudinally between a first end 25 and an opposite second end 26. The first and second ends 25, 26 are annular and centered on the longitudinal axis Z. The first end 25 has a first internal diameter d1 greater than a second internal or external diameter d2 of the second end 26.

[0047] The female cylindrical body 24 includes an internal housing 27. The internal housing 27 is annular and centered on the longitudinal axis Z. In particular, the internal housing 27 is located at the first end 25. Thus, the first end 25 is hollow.

[0048] The internal housing 27 is delimited by a grooved annular internal surface 28.

[0049] With reference to the figure 3The internal surface 28 thus has internal grooves 29. The internal grooves 29 are preferentially regularly distributed around the longitudinal axis Z. Each internal groove 29 extends longitudinally along the longitudinal axis Z. Each internal groove 29 thus has an elongated shape along a direction parallel to the longitudinal axis Z. Each internal groove 29 comprises an alternation of internal teeth 30 and internal grooves 31, around the longitudinal axis Z. Each internal tooth 30 has a vertex 30a extended by two lateral flanks 30b.

[0050] Each internal tooth 30 can have a profile of generally triangular or rectangular shape.

[0051] Each internal groove 31 is circumferentially delimited by two adjacent internal teeth 30. The space e1 delimited by two internal teeth defines the width of an internal groove 31.

[0052] The male cylindrical body 23 is free to rotate about the longitudinal axis Z. It extends longitudinally between a first end 32 and an opposite second end 33. The first end 32 may have longitudinal splines. The second end 33 is inserted into the internal housing 27 of the female cylindrical body 24. They cooperate by means of the splined connection.

[0053] For this purpose, the transmission shaft 22 further comprises a first splined section 34. As also visible on the figure 4 The first section 34 is annular and centered on the longitudinal axis Z. It is located coaxially around the male cylindrical body 23 and is rotationally fixed to this male cylindrical body 23. In particular, the first section 34 is located at the second longitudinal end 33 of the male cylindrical body 23. The first section 34 may have a diameter equal to or greater than the diameter of the male cylindrical body 23.

[0054] In a particularly preferred manner, the first section 34 and the male cylindrical body 23 form a single piece and are thus made from a single material. With reference to the figure 5 The first section 34 comprises a peripheral edge 35 and lateral sides 36. The peripheral edge 35 is annular and centered on the longitudinal axis Z. The lateral sides 36 are also annular and centered on the longitudinal axis Z and are located on either side of the peripheral edge 35.

[0055] At least one of the lateral sides 36 may include at least one housing 37. Advantageously, at least one of the lateral sides 36 may include two housings 37 which are diametrically opposed along the longitudinal axis Z. Each housing 37 has a curved shape.

[0056] The first section 34 further includes first grooves 38. The first grooves 38 extend longitudinally along the longitudinal axis Z and along the first section 34. The first grooves 38 are regularly distributed around the longitudinal axis Z. They are formed, for example, on the peripheral edge 35.

[0057] Each first groove 38 comprises an alternation around the longitudinal axis Z of first teeth 39 and first grooves 40.

[0058] Each first tooth 39 has a summit 39a extended by two lateral flanks 39b.

[0059] Each first tooth 39 can have a profile of general triangular or rectangular shape.

[0060] Each first groove 40 is circumferentially delimited by two adjacent first teeth 39.

[0061] As seen on the figure 3, the first grooves 38 of the male cylindrical body 23 cooperate with the internal grooves 39 of the female cylindrical body 24. In particular, the first teeth 39 are inserted into the internal grooves 31 of the internal grooves 29.

[0062] Such cooperation via splines allows the transmission of rotational motion from the male cylindrical body 23 to the female cylindrical body 24. However, the width of the first teeth 39 is less than the width e1 of the internal grooves 31. There is thus a defined angular clearance j between a first tooth 39 and an adjacent internal tooth 30. This angular clearance is responsible for knocking, dynamic overtorque, and torsional dynamics, which are exacerbated by the alternating phases of power injection and extraction during which the transmission shafts 22 are used.

[0063] For this purpose, the transmission shaft 22 according to the invention further comprises a second splined section 41 and advantageously a third splined section 42.

[0064] As seen on the figure 4 for example, the second and third sections 41, 42 are located coaxially around the male cylindrical body 23 and on either side of the first section 34.

[0065] With reference to the figure 6 The second section 41 is annular and centered on the longitudinal axis Z. It includes second splines 43. The second splines 43 extend longitudinally along the longitudinal axis Z and along the second section 41. The second splines 43 are regularly distributed around the longitudinal axis Z.

[0066] Each second groove 43 comprises an alternation around the longitudinal axis Z of second teeth 44 and second grooves 45.

[0067] Each second tooth 44 has a summit 44a extended by two lateral flanks 44b.

[0068] Each second tooth 44 may have a generally triangular or rectangular profile. Preferably, the profile of each second tooth 44 is identical to the profile of the first teeth 39. The number of second teeth 44 is identical to the number of first teeth 39. Each second groove 45 is circumferentially delimited by two adjacent second teeth 44.

[0069] The third section 42 is annular and centered on the longitudinal axis Z. It includes third splines 46. The third splines 46 extend longitudinally along the longitudinal axis Z and along the third section 42. The third splines 46 are regularly distributed around the longitudinal axis Z.

[0070] Each third groove 46 comprises an alternation around the longitudinal axis Z of third teeth 47 and third grooves 48.

[0071] Each third tooth 47 has a summit 47a extended by two lateral flanks 47b.

[0072] Each third tooth 47 may have a generally triangular or rectangular profile. Preferably, the profile of each third tooth 47 is identical to the profile of the first teeth 39 and the second teeth 43. The number of third teeth 47 is identical to the number of first teeth 39.

[0073] Each third groove 48 is circumferentially delimited by two adjacent third teeth 47.

[0074] The second and third sections 41, 42 are rotationally movable about the longitudinal axis X. The second and third sections 41, 42 are movable between a first position and a second position in which the second and third teeth 44, 47 are angularly offset relative to the first teeth 39. By "angularly offset," it is understood that the teeth have a different circumferential position. Preferably, the second and third teeth 44, 47 are angularly offset by less than half a pitch relative to the first teeth 39, a pitch being the inter-tooth distance e1 between two adjacent first teeth 39.

[0075] To ensure the movement of the second and third sections 41, 42 in rotation around the longitudinal axis X, the transmission shaft 22 further includes an elastic means 49 capable of stressing the second and third sections 41, 42 in rotation from the first to the second position.

[0076] The elastic means 49 comprises, for example, a first spring 49a and advantageously a second spring 49b suitable for applying stress to the second section 41. The elastic means 49 may also include third and fourth springs 49c, 49d suitable for applying stress to the third section 42. The first and second springs 49a, 49b are arranged in recesses 37 of a first lateral flank 36 of the first section 34. They are diametrically opposed. They mechanically connect the first section 34 to the second section 41. The third and fourth springs 49c, 49d are arranged in recesses 37 of a second lateral flank 36 of the first section 34. They are diametrically opposed. They mechanically connect the first section 34 to the third section 42.

[0077] The transmission shaft 22 advantageously comprises at least one axial stop 50 connected to the first spring 49a. Advantageously, the transmission shaft 22 comprises a second axial stop 51 connected to the second spring 49b. The first and second axial stops 50, 51 are diametrically opposed and located in the housing 37.

[0078] The transmission shaft 22 advantageously comprises at least one third axial stop 52 connected to the third spring 49c and a fourth axial stop 53 connected to the fourth spring 49d. The third and fourth axial stops 52, 53 being diametrically opposed and located in the housing 37.

[0079] With reference to the figure 7, the transmission shaft 22 may further include annular axial stops 54, 55 mounted around the male cylindrical body 23, the second and third sections 41, 42 being located axially between the first section 34 and the axial stops 54, 55 in order to maintain the second and third sections in axial position.

[0080] With reference to the figure 3 , in the mounting position of the male cylindrical body 23 in the female cylindrical body 24, the second teeth 44 and advantageously the third teeth 47 fill the gap j defined between the first teeth 39 and the internal teeth 30. Advantageously, the second teeth 44 and advantageously the third teeth 47 are pressed against the internal teeth 30.

[0081] Thanks to the second section 41 and the elastically deformable means 49, the play j between the male and female splines is filled, thus reducing rattles and torque oscillations.

[0082] The transmission shaft 22 is thus more mechanically robust, particularly to withstand alternating phases of injection and power extraction.

[0083] A method for preparing the transmission shaft 22 will now be described.

[0084] This preparation process includes the following steps: (a) Provide the male cylindrical body 23 with the first section 34, (b) mount the second and optionally third sections 41, 42 around the male cylindrical body 23, on either side of the first section 34, (c) apply the elastic means to drive the second and optionally third sections 41, 42 from the first position to the second position. Advantageously, the second and third sections 41, 42 are driven in rotation about the longitudinal axis Z in opposite directions. This allows for anticipating torque reversals in both directions of rotation.

[0085] A method for mounting the transmission shaft 22 will now be described.

[0086] This assembly process includes the following steps: (a') prepare the transmission shaft according to steps (a) to (c), (b') mount the male cylindrical body 23 in the female cylindrical body 24. During step (b'), the second teeth 44 and advantageously the third teeth 47 fill the gap j defined between the first teeth 39 and the internal teeth 30.

Claims

1. Transmission shaft (22) for an aircraft turbomachine (1), the transmission shaft (22) having a longitudinal axis (Z) and comprising: - a male cylindrical body (23) extending around and along the longitudinal axis (Z), - a first splined section (34) arranged coaxially around the male cylindrical body (23) and having first longitudinal splines (38) regularly distributed around the longitudinal axis (Z) and comprising an alternation of first teeth (39) and first grooves (40), the first section (34) being rotationally fixed to the male cylindrical body (23), characterized in thatthe transmission shaft (22) further comprises: - a second splined section (41) arranged coaxially around the male cylindrical body (23), the second section (41) having longitudinal second splines (43) regularly distributed around the longitudinal axis (Z) and comprising an alternation of second teeth (44) and second grooves (45), the second section (41) being stressed by an elastic element (49) from a first position to a second position in which the second teeth (44) are angularly offset with respect to the first teeth (39).

2. Tree according to the preceding claim, characterized in that the elastic element (49) includes at least a first spring (49a) mechanically connecting the first and second sections (34, 41).

3. Tree according to the preceding claim, characterized in thatthe elastic element (49) includes a second spring (49b) diametrically opposite the first spring (49a) and mechanically connecting the first and second sections (34, 41).

4. Tree according to claim 2 or 3, characterized in that the first section (34) includes an annular lateral flank (36) having at least a first housing (37) for receiving the first spring (49a) and optionally a second housing (37) for receiving the second spring (49b).

5. Tree according to any one of the preceding claims, characterized in that in the second position, the second teeth (44) are angularly offset by less than half a step relative to the first teeth (39), a step being the inter-tooth distance between two adjacent first teeth (39).

6. Tree according to any one of the preceding claims, characterized in that it includes at least one axial stop (50) connected to the elastic means (49).

7. Tree according to any one of the preceding claims, characterized in that it includes a third section (42) arranged coaxially around the male cylindrical body (23), the third section (42) having longitudinal third grooves (46) distributed around the longitudinal axis (Z) and comprising an alternation of third teeth (47) and third grooves (48), the first section (34) being arranged axially between the second and third sections (41, 42), the third section (42) being stressed by a second elastic element (49b) from a first position to a second position in which the third teeth (47) are angularly offset with respect to the first teeth (39).

8. Tree according to the preceding claim, characterized in that in the second position, the third teeth (47) are aligned angularly with the second teeth (44).

9. Tree according to any one of the preceding claims, characterized in thatIt comprises a female cylindrical body (24) having an annular internal housing (27) into which the male cylindrical body (23) is inserted and longitudinal internal grooves (29) cooperating with the first and second grooves (39, 44), the internal grooves (29) comprising an alternation of internal teeth (30) and internal grooves (31), the first teeth (39) being inserted into the internal grooves (30) and the second teeth (44) filling a defined angular gap (j) between the first teeth (39) and the internal teeth (30).

10. Tree according to the preceding claim, characterized in that the second teeth (44) are pressed against the inner teeth (30).

11. Method for preparing a transmission shaft (22) according to any one of the preceding claims, characterized in thatIt includes the following steps: (a) providing the male cylindrical body (23) on which the first section (34) is located, (b) providing the second section (41), and (c) applying the elastic means to drive the second section (41) from the first position to the second position.

12. Method of mounting a transmission shaft (22) according to any one of claims 1 to 8 in combination with claim 9, characterized in that It comprises the following steps: (a') preparing the transmission shaft (22) according to the preparation method of claim 11, (b') providing the female cylindrical body (24), and (c') inserting the male cylindrical body (23) into the female cylindrical body (24), the second teeth (44) filling the gap (j) defined between the first teeth (39) and the internal teeth (30).

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